curve #2244

y² + xy + y = x³ − 12784878141239x + 17499481905495051686

a-invariants: [1, 0, 1, -12784878141239, 17499481905495051686]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5270706210
discriminant (Δ): 1450414578896069322354823515821771052900
Faltings height: 6.3519
naive height: 102.1515
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 41, 101
regulator: 3.416284639767081330315646780077666031065
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:24 UTC
last updated: 2026-09-26 19:49:24 UTC

Witness: 1 independent point log in to add more points →

(2202105, 155209192)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=41; A=(3q-p)(p+q)^3=994555, B=-(p+3q)(p-q)^3=25254747. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 19:49:24 UTC · history